- Cankaya University Journal of Science and Engineering
- Vol: 18 Issue: 2
- Riemann Solutions (LCS)n-Manifolds Admitting Different Semi-Symmetric Structures
Riemann Solutions (LCS)n-Manifolds Admitting Different Semi-Symmetric Structures
Authors : Ashoke Das, Ashis Biswas, Bappaditya Debnath
Pages : 72-80
View : 10 | Download : 3
Publication Date : 2021-11-01
Article Type : Research
Abstract :The object of the present paper is to study the Riemannian solitons on (LCS)nmanifolds and we observed in this case the Riemann soliton on M is shrinking, steady or expanding according to α 2−ρ being positive, zero or negative respectively. Here also we discussed the Riemann solitons in (LCS)n-manifold admitting (i) R·C = 0, R·K = 0, (ii) E ·C = 0, E ·K = 0, (iii) R·R = 0, R·P = 0, R·E = 0, R·P ∗ = 0, R·M = 0, R ·Wi =0, R ·W∗ i = 0, (iv) E ·R = 0, E ·P = 0, E · E = 0, E ·P ∗ = 0, E ·M = 0, E · Wi = 0 and E · W∗ i = 0.( for all i = 1, 2, ....9). We found that the Riemann soliton on M is shrinking, steady or expanding according to the conditions (i) α 2 − ρ being positive, zero or negative respectively, (ii) [k(n−1) (n − 2) (1+α 2−ρ)−kr−r] being positive, zero or negative respectively and (iv) α 2 − ρ being negative, zero or positive. But for the condition (iii) the Riemann soliton on M is always steady.Keywords : Reimannian Solution, (LCS)n-manifold, semi-symetric structure